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Weber's Formula

Weber's formula is given by

1/(2p^2)e^(-(a^2+b^2)/(4p^2))I_nu((ab)/(2p^2))=int_0^inftye^(-p^2t^2)J_nu(at)J_nu(bt)tdt,

where Re[nu]>-1, |argp|<pi/4, and a, b>0, J_nu(z) is a Bessel function of the first kind, and I_nu(z) is a modified Bessel function of the first kind.

See also

Bessel Function of the First Kind, Modified Bessel Function of the First Kind

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References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1476, 1980.

Referenced on Wolfram|Alpha

Weber's Formula

Cite this as:

Weisstein, Eric W. "Weber's Formula." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WebersFormula.html

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